Abstract

Shear-induced self-diffusion of fibers suspended in an incompressible Newtonian fluid in simple shear flow at low Reynolds number is studied by simulation. Two models are employed: a linked rigid rod model and a bead chain model.Hydrodynamic interactions are neglected in both models. The shear-induced diffusivity of suspensions of fibers increases with increasing concentration and increasing static friction between contacts. The diffusivities in both the gradient and vorticity directions are larger for suspensions of curved fibers than for suspensions of straight fibers. For suspensions of curved fibers, significant enhancements in the diffusivity in the gradient direction are observed. The enhanced diffusivities are attributed to fiber drift observed in prior work for isolated curved fibers [J. Wang, E. J. Tozzi, M. D. Graham, and D. J. Klingenberg, “Flipping, scooping, and spinning: Drift of rigid curved nonchiral fibers in simple shear flow,” Phys. Fluids24, 123304 (2012)]. Here, for some initial orientations, curved fibers will drift in the positive or negative gradient direction with nearly constant speed. In dilute suspensions, this drift occurs for a fraction of the fibers, which increases the mean-squared displacement in the gradient direction, and thus increases the diffusivity in the gradient direction.

This research was financially supported by USDA (NRI Award No. 2006-35504-17401 and AFRI Award NO. 2010-65504-20406). We also thank one of the reviewers for pointing out the empirical model in Fig. 16.